The present invention relates to the refining and conversion of the heavy fractions of hydrocarbon distillates containing, inter alia, sulphur impurities. It relates more particularly to a process which allows the conversion, at low pressure, at least in part, of a hydrocarbon charge, for example, a vacuum distillate obtained by direct distillation of a crude petroleum, into good quality petrol and diesel light fractions and into a heavier product which may be used as a charge for catalytic cracking in a conventional catalytic cracking plant in a fluidised bed and/or in a catalytic cracking plant in a fluidised bed comprising a double regeneration system and optionally a cooling system for the catalyst at the regeneration stage. The present invention also relates in one of these aspects to a process for the production of petrol and/or diesel comprising at least one catalytic cracking step in a fluidised bed.